IMO you either need to go all in or not at all. And by all in I mean your "web page" is nothing but a <canvas> tag and your non-web framework is handling basically everything. It's an unholy nightmare for many reasons but it would at least allow you to make a reliable self-contained system.

"We'll take your native constructs and jimmy them into some bastardized HTML" is almost always full of razor-sharp edge cases.